Three issues:
1. OBS should be called by any umpire who sees it. Although the base umpire has primary responsibility at 1B, PU is not "poaching" to get that.
2. Although F6 obstructed R2 in your 2nd play, the OBS is ignored because the ball is dead when foul, and no runners may advance on a dead ball. And it's different from INT because the INT prevents an out in foul territory or fair, but the OBS did not prevent a runner from advancing (the foul ball did).
3. Your smart-azz comment ("since this was a foul ball your runner is entitled to 2nd base, and I'll let him have it without the liability to be put out") escalated the situation by suggesting that the defense committed OBS and you weren't going to penalize it.
All you needed to say was, "Coach, the ball's dead when foul, and runners must return, so the OBS is ignored in this case." When he complains that 'fair ball' doesn't appear under the definition, you can explain that since the runner cannot legally advance on a foul ball, he can't possibly be obstructed.
The coach took the bait, and earned his reward, but you didn't have to troll for him.
